metric spaces

Let (M,d) be a metric space.
1. Choose x element of M. Show that a set U subset of M is a neighbourhood of x if and only if x is an element of the Interior of U
2. Prove that the intersection U intersection V of any two neighbourhoods U and V of a point x element of M is also a neighbourhood of x.

Let (M,d) be a metric space.
1. Choose x element of M. Show that a set U subset of M is a neighbourhood of x if and only if x is an element of the Interior of U
2. Prove that the intersection U intersection V of any two neighbourhoods U and V of a point x element of M is also a neighbourhood of x.

Thanks soo much. I am really struggling with this since it is the first time I am taking a course of this nature, so please go in steps
Thanks for the help

What is a neighborhood? Do you take the Bourbaki "set containing an open set containing the point" or just "open set containing point"